A relativized hierarchy of conjunctive normal forms
is introduced, recognizable and SAT decidable in polynomial
time. The corresponding hardness parameter, the first level
of inclusion in the hierarchy, is studied in detail, admitting
several characterizations, e.g., using pebble games, the space
complexity of (relativized) tree-like ... more >>>

We give the first extension of the result due to Paul, Pippenger,
Szemeredi and Trotter that deterministic linear time is distinct from
nondeterministic linear time. We show that DTIME(n \sqrt(log^{*}(n)))
\neq NTIME(n \sqrt(log^{*}(n))). We show that atleast one of the
following statements holds: (1) P \neq L ... more >>>

We provide a characterization of the resolution
width introduced in the context of Propositional Proof Complexity
in terms of the existential pebble game introduced
in the context of Finite Model Theory. The characterization
is tight and purely combinatorial. Our
first application of this result is a surprising
proof that the ... more >>>

We define a collection of Prover-Delayer games that characterize certain subsystems of resolution. This allows us to give some natural criteria which guarantee lower bounds on the resolution width of a formula, and to extend these results to formulas of unbounded initial width.

We also use games to give upper ... more >>>

The last decade has seen a revival of interest in pebble games in the
context of proof complexity. Pebbling has proven to be a useful tool
for studying resolution-based proof systems when comparing the
strength of different subsystems, showing bounds on proof space, and
establishing size-space trade-offs. The typical approach ... more >>>

The two-player pebble game of Dymond–Tompa is identified as a barrier for existing techniques to save space or to speed up parallel algorithms for evaluation problems.

Many combinatorial lower bounds to study L versus NL and NC versus P under different restricted settings scale in the same way as the ... more >>>

We establish an exactly tight relation between reversible pebblings of graphs and Nullstellensatz refutations of pebbling formulas, showing that a graph $G$ can be reversibly pebbled in time $t$ and space $s$ if and only if there is a Nullstellensatz refutation of the pebbling formula over $G$ in size $t+1$ ... more >>>